There are five I know of, and they're called writing systems, and romanji/rōmaji is just the word for the romanisation of Japanese.
Now, GunSaberSeraph, the rest of my post concerns you:
Kanji — Japan decided it'd steal Chinese symbols at some point in history. A good start would be learning the "most common 2000 kanji used in newspapers" as they are known. Yes, seriously, two bloody thousand at bare minimum. Reading names is what will stump you good and hard, but just remember the Japanese are still learning how to read this stuff in grade 9. xD
Man'yōgana — Chinese symbols used for their sounds rather than meaning, eventually turned into short-form-like writing, becoming hiragana and katakana. Completely obsolete (like the English thorn letter :B), learning it will only make you able to read really old manuscripts, which is not what you're learning Japanese for. xD
Hentaigana — Archaic writing system in the same or a similar league as hiragana and katakana. Don't worry about this one, it's rarely used even in Japan, definitely never in its games.
Hiragana — Just your bog standard writing, but Japanese.
Katakana — Easiest one to read and write (in my opinion), usually used for writing foreign words.
Laugh at hentaigana if you must.
Wikipedia has very useful tables of hiragana and katakana, it'd be best to master those first. Many simpler games like Pokemon only use these two systems (or even only one of them). Wikipedia also has some learning resources at the bottom of the pages, I think.
